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 Call number: SPRINGER-1996-9789400902831:ONLINE Show nearby items on shelf Title: Trigonometric Fourier Series and Their Conjugates Author(s): Levan Zhizhiashvili Date: 1996 Size: 1 online resource (308 p.) Note: 10.1007/978-94-009-0283-1 Contents: Preface -- 1 Simple Trigonometric Series -- I. The Conjugation Operator and the Hilbert Transform -- II. Pointwise Convergence and Summability of Trigonometric Series -- III. Convergence and Summability of Trigonometric Fourier Series and Their Conjugates in the Spaces $$L^p \left( T \right),p \in \left] {0, + \infty } \right[$$ -- IV. Some Approximating Properties of Cesaro Means of the Series $$\sigma \left[ f \right]$$ and $$\bar \sigma \left[ f \right]$$ -- 2 Multiple Trigonometric Series -- I. Conjugate Functions and Hilbert Transforms of Functions of Several Variables -- II. Convergence and Summability at a Point or Almost Everywhere of Multiple Trigonometric Fourier Series and Their Conjugates -- III. Some Approximating Properties of n-Fold Cesaro Means of the Series $$\sigma _n \left[ f \right]$$ and $$\sigma _n \left[ {f,B} \right]$$ -- IV. Convergence and Summability of Multiple Trigonometric Fourier Series and Their Conjugates in the Spaces $$L^p \left( {T^n } \right),p \in \left] {0, + \infty } \right]$$ -- V. Summability of Series $$\sigma _2 \left[ f \right]$$ and $$\bar \sigma _2 \left[ {f,B} \right]$$ by a Method of the Marcinkiewicz Type ISBN: 9789400902831 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Mathematics and Its Applications : 372 Keywords: Mathematics , Approximation theory , Fourier analysis , Integral transforms , Operational calculus , Functions of real variables , Sequences (Mathematics) , Mathematics , Fourier Analysis , Approximations and Expansions , Integral Transforms, Operational Calculus , Sequences, Series, Summability , Real Functions Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE

 Call number: SPRINGER-1995-9789401102131:ONLINE Show nearby items on shelf Title: Ramified Integrals, Singularities and Lacunas Author(s): V. A Vassiliev Date: 1995 Size: 1 online resource (294 p.) Note: 10.1007/978-94-011-0213-1 Contents: I. Picard—Lefschetz—Pham theory and singularity theory -- § 1. Gauss-Manin connection in the homological bundles. Monodromy and variation operators -- § 2. The Picard-Lefschetz formula. The Leray tube operator -- § 3. Local monodromy of isolated singularities of holomorphic functions -- § 4. Intersection form and complex conjugation in the vanishing homology of real singularities in two variables -- § 5. Classification of real and complex singularities of functions -- § 6. Lyashko-Looijenga covering and its generalizations -- § 7. Complements of discriminants of real simple singularities (after E. Looijenga) -- § 8. Stratifications. Semialgebraic, semianalytic and subanalytic sets -- § 9. Pham’s formulae -- § 10. Monodromy of hyperplane sections -- § 11. Stabilization of local monodromy and variation of hyperplane sections close to strata of positive dimension (stratified Picard-Lefschetz theory) -- § 12. Homology of local systems. Twisted Picard-Lefschetz formulae -- § 13. Singularities of complete intersections and their local monodromy groups -- II. Newton’s theorem on the nonintegrability of ovals -- § 1. Stating the problems and the main results -- § 2. Reduction of the integrability problem to the (generalized) PicardLefschetz theory -- § 3. The element “cap” -- § 4. Ramification of integration cycles close to nonsingular points. Generating functions and generating families of smooth hypersurfaces -- § 5. Obstructions to integrability arising from the cuspidal edges. Proof of Theorem 1.8 -- § 6. Obstructions to integrability arising from the asymptotic hyperplanes. Proof of Theorem 1.9 -- § 7. Several open problems -- III. Newton’s potential of algebraic layers -- § 1. Theorems of Newton and Ivory -- § 2. Potentials of hyperbolic layers are polynomial in the hyperbolicity domains (after Arnold and Givental) -- § 3. Proofs of Main Theorems 1 and 2 -- § 4. Description of the small monodromy group -- § 5. Proof of Main Theorem 3 -- IV. Lacunas and the local Petrovski$$\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\smile}}}{I}$$ condition for hyperbolic differential operators with constant coefficients -- § 0. Hyperbolic polynomials -- § 1. Hyperbolic operators and hyperbolic polynomials. Sharpness, diffusion and lacunas -- § 2. Generating functions and generating families of wave fronts for hyperbolic operators with constant coefficients. Classification of the singular points of wave fronts -- § 3. Local lacunas close to nonsingular points of fronts and to singularities A2, A3 (after Davydova, Borovikov and Gárding) -- § 4. Petrovskii and Leray cycles. The Herglotz-Petrovskii—Leray formula and the Petrovskii condition for global lacunas -- § 5. Local Petrovskii condition and local Petrovskii cycle. The local Petrovskii condition implies sharpness (after Atiyah, Bott and Gárding) -- § 6. Sharpness implies the local Petrovskii condition close to discrete-type points of wave fronts of strictly hyperbolic operators -- § 7. The local Petrovskii condition may be stronger than the sharpness close to singular points not of discrete type -- § 8. Normal forms of nonsharpness close to singularities of wave fronts (after A.N. Varchenko) -- § 9. Several problems -- V. Calculation of local Petrovski$$\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\smile}}}{I}$$ cycles and enumeration of local lacunas close to real function singularities -- § 1. Main theorems -- § 2. Local lacunas close to singularities from the classification tables -- § 3. Calculation of the even local Petrovskii class -- § 4. Calculation of the odd local Petrovskii class -- § 5. Stabilization of the local Petrovskii classes. Proof of Theorem 1.5 -- § 6. Local lacunas close to simple singularities -- § 7. Geometrical criterion for sharpness close to simple singularities -- § 8. A program for counting topologically different morsifications of a real singularity -- § 9. More detailed description of the algorithm -- Appendix: a FORTRAN program searching for the lacunas and enumerating the morsifications of real function singularities ISBN: 9789401102131 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Mathematics and Its Applications : 315 Keywords: Mathematics , Algebraic geometry , Integral transforms , Operational calculus , Partial differential equations , Potential theory (Mathematics) , Manifolds (Mathematics) , Complex manifolds , Mathematics , Integral Transforms, Operational Calculus , Algebraic Geometry , Partial Differential Equations , Manifolds and Cell Complexes (incl. Diff.Topology) , Potential Theory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE

 Call number: SPRINGER-1994-9789401111966:ONLINE Show nearby items on shelf Title: The Hypergeometric Approach to Integral Transforms and Convolutions Author(s): Semen B Yakubovich Date: 1994 Size: 1 online resource (324 p.) Note: 10.1007/978-94-011-1196-6 Contents: 1 Preliminaries -- 1.1 Some special functions -- 1.2 Integral transforms -- 2 Mellin Convolution Type Transforms With Arbitrary Kernels -- 2.1 General Fourier kernels -- 2.2 Examples of the Fourier kernels -- 2.3 Watson type kernels -- 2.4 Bilateral Watson transforms -- 2.5 Multidimensional Watson transforms -- 3 H- and G-transforms -- 3.1 Mellin convolution type transform with Fox’s H-function as a kernel -- 3.2 Mellin convolution type transforms with Meijer’s G-function as a kernel -- 3.3 The Erdelyi-Kober fractional integration operators -- 4 The Generalized H- and G-transforms -- 4.1 The generalized H-transform -- 4.2 The generalized G-transform -- 4.3 Composition structure of generalized H- and G-transforms -- 5 The Generating Operators of Generalized H-transforms -- 5.1 Generating operators in the space ?Mc,??1 -- 5.2 Examples of the generating operators -- 6 The Kontorovich-Lebedev Transform -- 6.1 The Kontorovich-Lebedev transform: notion, existence and inversion theorems in Mc,??1 (L) spaces -- 6.2 The Kontorovich-Lebedev transform in weighted L-spaces -- 6.3 The Kontorovich-Lebedev transform in weighted L2 spaces -- 6.4 The Kontorovich-Lebedev transform of distributions -- 6.5 The Kontorovich-Lebedev transform in Lp-spaces -- 7 General W-transform and its Particular Cases -- 7.1 General G-transform with respect to an index of the Kontorovich-Lebedev type -- 7.2 General W-transform and its composition structure -- 7.3 Some particular cases of W-transform and their properties -- 7.4 F3-transform -- 7.5 L2-theory of the Kontorovich-Lebedev type index transforms -- 8 Composition Theorems of Plancherel Type for Index Transforms -- 8.1 Compositions with symmetric weight -- 8.2 Compositions with non-symmetric weight -- 8.3 Constructions of index transforms in terms of Mellin integrals -- 9 Some Examples of Index Transforms and Their New Properties -- 9.1 The Kontorovich-Lebedev like composition transforms -- 9.2 Some index transforms with symmetric kernels -- 9.3 The $$\Re$$ and $$\Im -$$ index transforms -- 10 Applications to Evaluation of Index Integrals -- 10.1 Some useful representations and identities -- 10.2 Some general index integrals -- 11 Convolutions of Generalized H-transforms -- 11.1 H-convolutions -- 11.2 Examples of H-convolutions -- 12 Generalization of the Notion of Convolution -- 12.1 Generalized H-convolutions -- 12.2 Generalized G-convolutions -- 13 Leibniz Rules and Their Integral Analogues -- 13.1 General Leibniz rules -- 13.2 Modified Leibniz rule -- 13.3 Leibniz rule for the Erdelyi-Kober fractional differential operator -- 13.4 Modification of the Leibniz rule for the Erdelyi-Kober fractional differential operator -- 13.5 Integral analogues of Leibniz rules -- 14 Convolutions of Generating Operators -- 14.1 Convolutions in the Dimovski sense. General results -- 14.2 Examples of convolutions in the Dimovski sense -- 15 Convolution of the Kontorovich-Lebedev Transform -- 15.1 Definition and some properties of a convolution for the Kontorovich-Lebedev transform -- 15.2 The basic property of convolution. Analogues with the Parseval equality -- 15.3 On the inversion of the Kontorovich-Lebedev transform in the ring L? -- 15.4 The space L? as the commutative normed ring of functions with exponential growth -- 16 Convolutions of the General Index Transforms -- 16.1 Convolutions of the Kontorovich-Lebedev type transforms -- 16.2 The convolutions for the Mehler-Fock and the Lebedev-Skalskaya transforms -- 16.3 The convolution of the Wimp-Yakubovich type index transform -- 17 Applications of the Kontorovich-Lebedev type Convolutions to Integral Equations -- 17.1 Kontorovich-Lebedev convolution equations of the second kind -- 17.2 General composition convolution equations -- 17.3 Some results on the homogeneous equation -- 18 Convolutional Ring C? -- 18.1 Multiple Erdelyi-Kober fractional integrodifferential operators -- 18.2 Convolutional ring C? -- 19 The Fields of the Convolution Quotients -- 19.1 Extension of the ring (C?,?*,+) -- 19.2 Extension of the ring (L?,*,+) -- 20 The Cauchy Problem for Erdelyi-Kober Operators -- 20.1 General scheme -- 20.2 Differential equations of fractional order -- 20.3 Differential equations of hyper-Bessel type -- 21 Operational Method of Solution of some Convolution Equations -- 21.1 Integral equations of Volterra type -- 21.2 Integral equations of second kind with Kontorovich-Lebedev convolution -- References -- Author Index -- Notations ISBN: 9789401111966 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Mathematics and Its Applications : 287 Keywords: Mathematics , Integral equations , Integral transforms , Operational calculus , Special functions , Mathematics , Integral Transforms, Operational Calculus , Special Functions , Integral Equations Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. 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 Call number: SPRINGER-1993-9781461203155:ONLINE Show nearby items on shelf Title: Integrable Systems The Verdier Memorial Conference Actes du Colloque International de Luminy Author(s): Date: 1993 Size: 1 online resource (370 p.) Note: 10.1007/978-1-4612-0315-5 Contents: Hommage à Jean-Louis Verdier: au jardin des systèmes intégrables -- I. Algebro-Geometric Methods and ?-Functions -- Compactified Jacobians of Tangential Covers -- Heisenberg Action and Verlinde Formulas -- Hyperelliptic Curves that Generate Constant Mean Curvature Tori in ?3 -- Modular Forms as ?-Functions for Certain Integrable Reductions of the Yang-Mills Equations -- The ?-Functions of the gAKNS Equations -- On Segal-Wilson’s Definition of the ?-Function and Hierarchies AKNS-D and mcKP -- The Boundary of Isospectral Manifolds, Bäcklund Transforms and Regularization -- II. Hamiltonian Methods -- The Geometry of the Full Kostant-Toda Lattice -- Deformations of a Hamiltonian Action of a Compact Lie Group -- Linear-Quadratic Metrics “Approximate” any Nondegenerate, Integrable Riemannian Metric on the 2-Sphere and the 2-Torus -- Canonical Forms for Bihamiltonian Systems -- Bihamiltonian Manifolds and Sato’s Equations -- III. Solvable Lattice Models -- Generalized Chiral Potts Models and Minimal Cyclic Representations of $${U_q}(\widehat{gl}(n,C))$$) -- Infinite Discrete Symmetry Group for the Yang-Baxter Equations and their Higher Dimensional Generalizations -- IV. Topological Field Theory -- Integrable Systems and Classification of 2-Dimensional Topological Field Theories -- List of Participants ISBN: 9781461203155 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Progress in Mathematics : 115 Keywords: Mathematics , Algebra , Integral transforms , Operational calculus , Mathematics , General Algebraic Systems , Integral Transforms, Operational Calculus Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE

 Call number: SPRINGER-1992-9789401124249:ONLINE Show nearby items on shelf Title: The Mellin Transformation and Fuchsian Type Partial Differential Equations Author(s): Zofia Szmydt Date: 1992 Size: 1 online resource (222 p.) Note: 10.1007/978-94-011-2424-9 Contents: I. Introduction -- §1. Terminology and notation -- §2. Elementary facts on complex topological vector spaces -- Exercise -- §3. A review of basic facts in the theory of distributions -- Exercises -- II. Mellin distributions and the Mellin transformation -- §4. The Fourier and the Fourier-Mellin transformations -- Exercises -- §5. The spaces of Mellin distributions with support in a polyinterval -- Exercises -- §6. Operations of multiplication and differentiation in the space of Mellin distributions -- Exercises -- §7. The Mellin transformation in the space of Mellin distributions -- Exercises -- §8. The structure of Mellin distributions -- Exercises -- §9. Paley-Wiener type theorems for the Mellin transformation -- Exercises -- §10. Mellin transforms of cut-off functions (continued) -- Exercises -- §11. Important subspaces of Mellin distributions -- Exercises -- §12. The modified Cauchy transformation -- Exercises -- III. Fuchsian type singular operators -- §13. Fuchsian type ordinary differential operators -- Exercises -- §14. Elliptic Fuchsian type partial differential equations in spaces % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaacI % cacaWG4bWaaSaaaeaacaWGKbaabaGaamizaiaadIhaaaGaaiykaiaa % dwhacqGH9aqpcaWGMbaaaa!3EE9!$$P(x\frac{d}{{dx}})u = f$$ -- 2. Case of a proper cone -- Exercise -- §15. Fuchsian type partial differential equations in spaces with continuous radial asymptotics -- Appendix. Generalized smooth functions and theory of resurgent functions of Jean Ecalle -- 1. Introduction -- 2. Generalized Taylor expansions -- 3. Algebra of resurgent functions of Jean Ecalle -- 4. Applications -- List of Symbols ISBN: 9789401124249 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Mathematics and Its Applications (East European Series): 56 Keywords: Mathematics , Approximation theory , Functional analysis , Integral transforms , Operational calculus , Partial differential equations , Mathematics , Partial Differential Equations , Integral Transforms, Operational Calculus , Functional Analysis , Approximations and Expansions Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE

 Call number: SPRINGER-1988-9781461310556:ONLINE Show nearby items on shelf Title: Generalized Functions, Convergence Structures, and Their Applications Author(s): Date: 1988 Size: 1 online resource (464 p.) Note: 10.1007/978-1-4613-1055-6 Contents: Section I. Plenary Lectures -- Nonharmonic solutions of the Laplace equation -- Generalized functions multiplication of distributions applications to elasticity, elastoplasticity, fluid dynamics and acoustics -- Monads and convergence -- Simple applications of generalized functions in theoretical physics: the case of many-body perturbation expansions -- Laplace transforms of hyperfunctions: another foundation of the Heaviside operational calculus -- S-asymptotic of distributions -- The Wiener-Hopf equation in the Nevanlinna and Smirnov algebras and ultradistributions -- Section II. Generalized Functions -- On nonlinear systems of ordinary differential equations -- A new construction of continuous endomorphisms of the operator field -- Some comments on the Burzyk-Paley-Wiener theorem for regular operators -- Two theorems on the differentiation of regular convolution quotients -- Values on the topological boundary of tubes -- Abelian theorem for the distributional Stieltjes transformation -- Some results on the neutrix convolution product of distributions -- On generalized transcedental functions and distributional transforms -- An algebraic approach to distribution theories -- Products of Wiener functionals on an abstract Wiener space -- Convolution in K’{Mp}-spaces -- The problem of the jump and the Sokhotski formulas in the space of generalized functions on a segment of the real axis -- A generalized fractional calculus and integral transforms -- On the generalized Meijer transformation -- The construction of regular spaces and hyperspaces with respect to a particular operator -- Operational calculus with derivative ? = S2 -- Solvability of nonlinear operator equations with applications to hyperbolic equations -- Some important results of distribution theory -- Hyperbolic systems with discontinuous coefficients: examples -- Estimations for the solutions of operator linear differential equations -- Invariance of the Cauchy problem for distribution differential equations -- On the space $$\upsilon _{{\text{L}}^{\text{q}} }^{\prime\,^{\left( {{\text{M}}_{\text{p}} } \right)} }$$ , q ? [1, ?] -- Peetre’s theorem and generalized functions -- Infinite dimensional Fock spaces and an associated generalized Laplacian operator -- The n–dimensional Stieltjes transformation -- Colombeau’s generalized functions and non-standard analysis -- One product of distributions -- Abel summability for a distribution sampling theorem -- On the value of a distribution at a point -- Section III. Convergence Structures -- On interchange of limits -- Countability, completeness and the closed graph theorem -- Inductive limits of Riesz spaces -- Convergence completion of partially ordered groups -- Some results from nonlinear analysis in limit vector spaces -- Completions of Cauchy vector spaces -- Regular inductive limits -- Weak convergence in a K-space -- The Banach-Steinhaus theorem for ordered spaces -- Section IV. Open Problems -- Open problems -- Participants ISBN: 9781461310556 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Mathematics , Computer science , Mathematical analysis , Analysis (Mathematics) , Mathematics , Analysis , Computer Science, general Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE